Number Sense and Operations:

1.      Demonstrate an understanding of reason for the impossible division by zero. 

2.      Demonstrate an understanding of integers and their properties. 

3.      Demonstrate an understanding of special numbers (palindromes, triangular, etc.) 

4.      Demonstrate an understanding of the coordinate plane. 

5.      Relate the understanding of integers to real numbers. 

6.      Evaluate choices through estimation. 

7.      Estimate to validate solutions using fractions, decimals, percents, squares, etc. 

8.      Solve problems using percentage. 

Patterns, Relations and Algebra:

1.            Extend, represent, analyze, and generalize a variety of patterns, including arithmetic and geometric progressions, with tables, graphs, words, and when possible, symbolic expressions.

2.            Use tables, graphs, and equations to solve problem situations involving growth and decay, simple and compound interest. 

3.            Demonstrate understanding of the identity (-a)(-b) = ab.

4.            Identify the slope of a line with its steepness and as a constant rate of change from its table of values, equation, and graph.  Apply the concept of slope to the solution of problems.

·        Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b.

5.            Represent and solve linear equations and/or inequalities, with one or two variables using algebraic symbols.

6.            Explain and analyze-both quantitatively and qualitatively, using pictures, graphs charts or equations-how a change in one variable results in the change in another variable in functional relationships, e.g., C = p d, A = p r² (A as a function of r) 

7.            Use tables and graphs to represent and compare linear growth patterns.  In particular, compare rates of change and intercepts. 

Geometry:

1.            Analyze, apply and explain the relationship between the number of sides and the sums of interior and exterior angle measures of polygons.

2.            Identify, label parts of right triangle, polygons.   

·        Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.

3.            Demonstrate the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.

4.            Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.

5.            Use a straightedge, compass or other tools to formulate and test conjectures and to make geometric figures.

6.            Demonstrate transformational and coordinate geometry.

·        Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., show how tessellations transform under translations, reflections and rotations. 

7.            Use spatial relationships such as parallel faces to identify three-dimensional figures (e.g., pyramids) by their physical appearance and distinguishing attributes.

Measurement:

1.            Given the formulas, determine the surface area and volume of rectangular prisms, cylinders and spheres.  Use technology as appropriate.

2.            Use ratio and proportion (including scale factors) in the solution of problems, including those involving similar plane figures and indirect measurement.

Data Analysis, Statistics and Probability:

1.            Using models to predict central tendencies; statistical conclusions; misuses of data.

2.            Interpret information in graphs

·        Describe the characteristics and limitations of data sample.  Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling.

·        Select, create, interpret and utilize various tabular and graphical representations of data (e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box plots, histograms, tables and charts).  Differentiate between continuous and discrete data and ways to represent them.